An upper limb exoskeleton is a wearable robotic system that is physically linked to the arm of the human operators and its seven actuated degrees of freedom (DOF) match the seven DOF of the human arm. The stability of such a system is critical given the proximity of its human operator. A new PID controller is developed which guarantee asymptotic stability for this class of robotic manipulators. A simulation was used to assess the system performance given the theoretical results of the controller's parameters with a unique exoskeleton system (EXO-UL7). The simulation also verify the semi-global asymptotic stability of the system. The proposed methodology eliminates the need of the system's dynamics model for the purpose of designing the controller. It provides an analytical tool for the controller design that is traditionally preformed experimentally (parameter tuning).